Specific Impulse outside Earth

[Manilka]

Hello!

As I know if I have Isp in seconds and want to calculate specific impulse in m/sec, I must multiply Isp by g0 which is 9.8 m/sec^2 for Earth. But what will be g0 in case of other planets or in space?
Like should I use g0=1.6m/sec^2 for Moon or it still will be 9.8m/sec^2 no matter where are you?

Thanks in advance!

 

[perseus]

hello..:thumbup:

As I know if I have Isp in seconds and want to calculate specific impulse in m/sec, I must multiply Isp by g0 which is 9.8 m/sec^2

Always by definition of specific impulse:
It represents the force with respect to the amount of propellant used per unit time.[1] If the "amount" of propellant is given in terms of mass (such as in kilograms), then specific impulse has units of velocity. If it is given in terms of weight (such as in kiloponds or newtons)

---------- Post added at 03:36 PM ---------- Previous post was at 03:28 PM ----------

Isp=Vg/(9,8 m / seg ^ 2)

The mathematical relation that determines the flow of gases based on the area of neck nozzle (Sc), acceleration due to gravity (g), chamber pressure (Pc) and output (Ps), temperature (T), density (r), specific heat (Cesp), being the equivalent mechanical of heat to consider 427
Vg=√2xgx427xCespxTx[1-(Ps/Pc)^((Cesp-1)/Cesp)]

 

[Manilka]

Thanks a lot!

 

[kamaz]

Hello!
As I know if I have Isp in seconds and want to calculate specific impulse in m/sec, I must multiply Isp by g0 which is 9.8 m/sec^2 for Earth. But what will be g0 in case of other planets or in space?

If you want to calculate delta-v budget from the rocket equation, then you actually want to use exit velocity, v_e, in m/s:

v_e = g_0 * I_sp

...where g_0 is 9.8 m/s^2. Ultimately, both I_sp and v_e measure the same thing, which is a characteristic of the engine and so not dependent on its location. The reason people use I_sp (Earth-specific) intead of v_e (universal) is that it makes some engineering calculations easier:

This I_sp expressed in seconds is somewhat physically meaningful—if an engine's thrust could be adjusted to equal the initial weight of its propellant (measured at one standard gravity), then Isp is the duration the propellant would last.

http://en.wikipedia.org/wiki/Specific_impulse#Specific_impulse_in_seconds

...in other words, I_sp gives you burn time of a rocket stage with TWR=1 on Earth. So, when taking off from Earth, your stage with a given TWR will accelerate at TWR-1 standard gravities (i.e. (TWR-1)*g_0 [m/s^2]) and the fuel will be exhausted within I_sp/TWR seconds.

 

[francisdrake]

For practical reasons I always consider the Isp as velocity v_e in [m/s] as given above. This value is also used in Orbiter as the engine parameter, along with the thrust.

B.t.w. the exact value of g is 9.80665 m/s². This is defined value, as the gravity varies slighty all around Earth. For approximzation 9.81 m/s² is good enough.

 

[jedidia]

ike should I use g0=1.6m/sec^2 for Moon or it still will be 9.8m/sec^2 no matter where are you?

ISP in seconds or m/s (which is actually the exhaust velocity, and Orbiter handles ISP only in m/s) is merely a unit conversion, not related to the place where you are located. So you always have to use 9.81 to convert from one to the other.

 

[Urwumpe]

Actually, the SI unit of specific impulse is not m/s, but [math]\frac{N \cdot s}{kg}[/math] (impulse per unit of propellant mass).

If you then remember that one Newton as unit of Force is defined as [math]N = \frac{kg \cdot m}{s^2}[/math], you can easily see that specific impulse and average exhaust velocity really use the same unit and could be equivalent.

The TWR concept of seconds is pretty apologist, since it only works:

• On Earth,
• Near the surface,
• In regions of Earth with the same local gravity acceleration as Europe,
• And with only low horizontal velocities

Why? Because weight is not mass. Have a different apparent gravity, and weight force changes.

But for getting seconds as unit of specific impulse, you have to declare that weight and mass are the same. Really, really stupid. But then, many US citizens had become famous for doing really, really stupid things so long, that it became a tradition.

... Well, I'll also continue to call it "Schraubenzieher" (Screw puller) in German than the proper term "Schraubendreher" (screw driver).

 

[boogabooga]

Hello!
Like should I use g0=1.6m/sec^2 for Moon or it still will be 9.8m/sec^2 no matter where are you?

Yeah, so to answer the question treat 9.81 m/s^2 as an arbitrary constant to use everywhere.

 

[chopleta]

I know this post was several years ago but I recently had the same question as I was working on the development of a thruster for a lunar application. I thought I would share my findings since this site helped me understand my dilemma. The mass flow rate through the nozzle can be calculated several ways. On the moon, the nozzle exit pressure is zero and so it has an infinite expansion. In this case, the mass flow rate can be calculated as mdot = Fthrust x G/(c* x gamma), where G is a function of gamma for the propellant used and c* is the characteristic velocity. Notice how g0 does not appear in the equation at all. Now, mdot can also be calculated as mdot = Fthrust/(Isp x g0). If you plug in the numbers and calculate mdot both was you get the exact same answer only when you use g0=9.81 m/s^2. This confirms boogabooga's post that, in this case, g0 should be thought as an arbitrary constant to be used everywhere.

 

[francisdrake]

To my knowledge, measuring the ISP in [sec] dates back to the Apollo project. NASA had contractors, some of them using imperial units, some of them using the metric system. To avoid confusion, they agreed to state the ISP in [sec].

Then every engineer just had to multiply it with the gravity acceleration in their respective system to get the exhaust velocity. For example the imperial gravity is 32.17 ft/s^2.